Controllability Analysis and Degraded Control for a Class of Hexacopters Subject to Rotor Failures

This paper considers the controllability analysis and fault tolerant control problem for a class of hexacopters. It is shown that the considered hexacopter is uncontrollable when one rotor fails, even though the hexacopter is over-actuated and its controllability matrix is row full rank. According to this, a fault tolerant control strategy is proposed to control a degraded system, where the yaw states of the considered hexacopter are ignored. Theoretical analysis indicates that the degraded system is controllable if and only if the maximum lift of each rotor is greater than a certain value. The simulation and experiment results on a prototype hexacopter show the feasibility of our controllability analysis and degraded control strategy.Comment: 21 pages, 7 figures, submitted to Journal of Intelligent & Robotic System

Topics in Partially Linear Single-Index Models for Longitudinal Data

The partially linear single-index model is a semiparametric model proposed to the case when some predictors are linearly associated with the response variable, while some other predictors are nonlinearly associated with the response variable. It is widely used for its flexibility in statistical modeling. Furthermore, its generalized version is a generalization of some popular models such as the generalized linear model, the partially linear model and the single-index model. However, the proper estimation in partially linear single-index models for longitudinal data, where multiple measurements are observed for each subject, is still open to discussion. Our main purpose is to establish a unified estimation method for the longitudinal partially linear single-index model and its generalized version. With this question in mind, we propose a new iterative three-stage estimation method in partially linear single-index models and generalized partially linear single-index models for longitudinal data. With the proposed method, the within-subject correlation is properly taken into consideration in the estimation of both the parameters and the nonparametric single-index function. The parameter estimators are shown to be asymptotically semiparametric efficient. The asymptotic variance of the single-index function estimator is shown to be generally less than that of existing estimators. Simulation studies are performed to demonstrate the finite sample performance. Three real data examples are also analyzed to illustrate the methodology

Topics in Partially Linear Single-Index Models for Longitudinal Data

The partially linear single-index model is a semiparametric model proposed to the case when some predictors are linearly associated with the response variable, while some other predictors are nonlinearly associated with the response variable. It is widely used for its flexibility in statistical modeling. Furthermore, its generalized version is a generalization of some popular models such as the generalized linear model, the partially linear model and the single-index model. However, the proper estimation in partially linear single-index models for longitudinal data, where multiple measurements are observed for each subject, is still open to discussion. Our main purpose is to establish a unified estimation method for the longitudinal partially linear single-index model and its generalized version. With this question in mind, we propose a new iterative three-stage estimation method in partially linear single-index models and generalized partially linear single-index models for longitudinal data. With the proposed method, the within-subject correlation is properly taken into consideration in the estimation of both the parameters and the nonparametric single-index function. The parameter estimators are shown to be asymptotically semiparametric efficient. The asymptotic variance of the single-index function estimator is shown to be generally less than that of existing estimators. Simulation studies are performed to demonstrate the finite sample performance. Three real data examples are also analyzed to illustrate the methodology